Inverse-Moment Chiral Sum Rules

Abstract

A general class of inverse-moment sum rules was previously derived by the authors in a chiral perturbation theory (ChPT) study at two-loop order of the isospin and hypercharge vector-current propagators. Here, we address the evaluation of the inverse-moment sum rules in terms of existing data and theoretical constraints. Two kinds of sum rules are seen to occur, those which contain as-yet undetermined $\mathcal{O}(q^6)$ counterterms and those free of such quantities. We use the former to obtain phenomenological evaluations of two $\mathcal{O}(q^6)$ counterterms. Light is shed on the important but difficult issue regarding contributions of higher orders in the ChPT expansion.

Only changes: typo in Eq. (1) corrected and Ref. 15 expanded

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• Tests of the naturalness of the coupling constants in ChPT at order p^6
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• The Extraction of Light Quark Masses From Sum Rule Analyses of Axial and Vector Current Ward Identities
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• The DMO Sum Rule Revisited
• Determination of the NNLO low-energy constant $C_{93}$